List of top Mathematics Questions asked in JEE Main

A bag contains $30$ white balls and $10$ red balls. $16$ balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, the $\left(\frac{\text{mean} \; \text{of} \; X}{\text{standard} \; \text{deviation} \; \text{of} \; X }\right)$ is equal to :

In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is :In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is :

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn cards. Then P(X = 1) + P(X = 2) equals :

Let $S_n$ denote the sum of the first $n$ terms of an $A.P$. If $S_4 = 16$ and $S_6 = -48$, then $S_{10}$ is equal to :

A hyperbola has its centre at the origin, passes through the point $(4,2)$ and has transverse axis of length $4$ along the x-axis. Then the eccentricity of the hyperbola is :

If the truth value of the statement $P \to ( \sim p \vee r)$ is false(F), then the truth values of the statements $p, q, r$ are respectively :

The mean and the median of the following ten numbers in increasing order $10, 22, 26, 29, 34, x 42, 67, 70,\, y$ are $42$ and $35$ respectively, then $\frac{y}{x}$ is equal to :

The plane which bisects the line segment joining the points (-3,-3,4) and (3,7,6) at right angles, passes through which one of the following points ?

Two integers are selected at random from the set {1, 2,...., 11}. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is :

The plane through the intersection of the planes $x + y + z = 1$ and $2x + 3y - z + 4 = 0$ and parallel to y-axis also passes through the point :

The sum $1+ \frac{1^{3} +2^{3}}{1+2} + \frac{1^{3}+2^{3}+3^{3}}{1+2+3} +.... + \frac{1^{3} +2^{3}+3^{3} +....+15^{3}}{1+2+3+...+15} - \frac{1}{2} \left(1+2+3+...+15\right)$

Let $Z$ be the set of integers. If $A \, = \, \{ x \in Z : 2^{ (x+2) (x^2 - 5x + 6)} \}=1$ and $B \, = \, \{ \, x \in Z: -3 <2x -1 <9 \}$, then the number of subsets of the set $A \times B$, is :

Let $A$ and $B$ be two invertible matrices of order $3 \times 3$. If $\text{det} (ABA^T) = 8$ and $\text{det} (AB^{-1}) = 8$, then $\text{det} (BA^{-1} BT) $ is equal to :

Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of two balls and so on. If $99$ more identical balls are addded to the total number of balls used in forming the equilaterial triangle, then all these balls can be arranged in a square whose each side contains exactly $2$ balls less than the number of balls each side of the triangle contains. Then the number of balls used to form the equilateral triangle is :

The value of $\cot\left(\sum\limits^{19}_{n=1} \cot^{-1} \left(1+ \sum\limits^{n}_{p=1} 2p\right)\right) $ is :

Let $A(4,-4)$ and $B(9,6)$ be points on the parabola, $y^2 + 4x$. Let $C$ be chosen on the arc $AOB$ of the parabola, where $O$ is the origin, such that the area of $\Delta ACB$ is maximum. Then, the area (in s units) of $\Delta ACB$, is :

The value of the integral $\int \limits^{2}_{-2} \frac{\sin^{2}x}{\left[\frac{x}{\pi}\right] + \frac{1}{2}} dx $ (where [x] denotes the greatest integer less than $^{20}C_r$ or equal to x) is :

The value of $\int\limits^{\pi/2}_{-\pi/2} \frac{dx}{\left[x\right]+\left[\sin x\right]+4} $ where [t] denotes the greatest integer less than or equal to t, is :

The equation of the plane containing the $\frac{x}{2} = \frac{y}{3} =\frac{z}{4} $ and perpendicular to the plane containing the straight lines $\frac{x}{3} = \frac{y}{4} = \frac{z}{2} $ and $\frac{x}{4} = \frac{y}{2} = \frac{z}{3} $ is :

If \(\int \frac{dx}{x^3 (1+x^6)^{\frac{2}{3}}} = f(x) (1+ x^{6})^{\frac{1}{3}} + C\) where C is a constant of integration, then \(f(x)\) is equal to :

Let $\vec{a} = \hat{i} + \hat{j} + \sqrt{2} \hat{k} , \vec{b} = b_1 \hat{i} + b_2 \hat{j} + \sqrt{2} \hat{k}$ and $\vec{c} = 5 \hat{i} + \hat{j} + \sqrt{2} \hat{k}$ be three vectors such that the projection vector of $\vec{b}$ on $\vec{a}$ , If $\vec{a} + \vec{b}$ is perpendicular to $\vec{c}$, then $| \vec{b}|$ is equal to :

Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is :

A circle touching the x-axis at $(3, 0)$ and making an intercept of length $8$ on the y-axis passes through the point :